Optimized, the point is that there are lots of positions where you'd *love* to have your rook behind the pawn, but it's not in the cards. This one, assuming you look past the nice catch on move 31, is one of them. And there are lots more where there never was a chance to begin with.
I recently worked through (part of) the thirty pages Dvoretsky devotes to this sort of an endgame. Short answer is that it's right that the best chances usually involve stopping at the 6th rank and walking the king over. In this case, it also helps that it's a knight's pawn and not a rook pawn. That's because White has to prepare to eventually give up their rook for the advanced pawn. But meanwhile, they'll have won some or all of your kingside pawns, so your king has to get back in time to win a rook vs two-or-three pawns endgame. This would be harder if it were one file further away, but on the knight's file, it's often a win -- at least in practice. Theory, amazingly, still isn't completely settled on some of these, and people are still finding improbable wins in allegedly drawn endgames and vice versa. For instance, a drawing defense was apparently recently found to some endgames like this that involved White using their king to block Black's king from getting to b2.
Which chapter or pages is it in Dvoretsky's endgame manual? I will have a look and see if it helps me understand how to play these kinds of positions.
Sometimes I have fun and come off as a bigger jerk than I really am, so I'm glad you didn't take it too badly